Problem: Simplify the following expression: $ x = \dfrac{-y}{-10y - 3} + \dfrac{2}{7} $
Explanation: In order to add expressions, they must have a common denominator. Multiply the first expression by $\dfrac{7}{7}$ $ \dfrac{-y}{-10y - 3} \times \dfrac{7}{7} = \dfrac{-7y}{-70y - 21} $ Multiply the second expression by $\dfrac{-10y - 3}{-10y - 3}$ $ \dfrac{2}{7} \times \dfrac{-10y - 3}{-10y - 3} = \dfrac{-20y - 6}{-70y - 21} $ Therefore $ x = \dfrac{-7y}{-70y - 21} + \dfrac{-20y - 6}{-70y - 21} $ Now the expressions have the same denominator we can simply add the numerators: $x = \dfrac{-7y - 20y - 6}{-70y - 21} $ $x = \dfrac{-27y - 6}{-70y - 21}$ Simplify the expression by dividing the numerator and denominator by -1: $x = \dfrac{27y + 6}{70y + 21}$